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Measures of Agreement with Multiple Raters: Fréchet Variances and Inference.

Jonas Moss1

  • 1Department of Data Science and Analytics, BI Norwegian Business School, Oslo, Norway. jonas.moss.statistics@gmail.com.

Psychometrika
|January 8, 2024
PubMed
Summary

This study introduces Fréchet variances for multi-rater agreement analysis, generalizing disagreement functions. It also provides limit theory for g-wise weighted agreement coefficients and recommends arcsine or Fisher transforms for confidence intervals.

Keywords:
AC1Cohen kappaagreementinter-rater reliability

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Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • Measures of inter-rater agreement are crucial but vary in handling chance agreement, disagreement functions, and multiple raters.
  • Existing methods like Cohen's kappa and Fleiss's kappa have limitations, particularly with more than two raters.

Purpose of the Study:

  • To propose Fréchet variances as a method for handling multiple raters in agreement analysis.
  • To derive the limit theory for g-wise weighted agreement coefficients.
  • To recommend optimal methods for constructing confidence intervals for agreement coefficients.

Main Methods:

  • Utilizing Fréchet variances to generalize nominal, quadratic, and absolute value disagreement functions for multi-rater scenarios.
  • Deriving limit theory for g-wise weighted agreement coefficients with Cohen-type or Fleiss-type chance agreement.
  • Evaluating three confidence interval construction methods.

Main Results:

  • Fréchet variances provide an intuitive and generalized approach to disagreement measurement for multiple raters.
  • The derived limit theory applies to g-wise weighted agreement coefficients under specific conditions.
  • The arcsine transform and Fisher transform are recommended for calculating confidence intervals.

Conclusions:

  • Fréchet variances offer a robust solution for multi-rater agreement analysis.
  • The theoretical framework supports the use of g-wise weighted agreement coefficients.
  • Arcsine and Fisher transforms enhance the reliability of confidence intervals in agreement studies.